4|3x-1| + 3 > 11
4|3x-1| > 11-3
4|3x-1| > 8
|3x-1| > 2
3x-1>2 or 3x-1<-2
3x>2+1 3x<-2+1
3x>3 3x<-1
x>1 x<-1÷3
Solution: ]-♾️ , -1÷3 [ U ] 1,+♾️ [
Answer: x=13
Step-by-step explanation: Move all terms that don't contain x to the right side and solve.
Hope this helps you out! ☺
Answer:
The sum of the sequence 1+3+5+7+...1001 is 251001.
Step-by-step explanation:
Given sequence is 1 + 3 + 5 + 7 + ....+ 1001.
Here,
and so on upto ![a_n=1001](https://tex.z-dn.net/?f=a_n%3D1001)
Lets find the difference between each term
![a_1-a_0=3-1=2](https://tex.z-dn.net/?f=a_1-a_0%3D3-1%3D2)
![a_3-a_2=5-3=2](https://tex.z-dn.net/?f=a_3-a_2%3D5-3%3D2)
![a_4-a_3=7-5=2](https://tex.z-dn.net/?f=a_4-a_3%3D7-5%3D2)
We see that the difference between each term of the given sequence is 2 . Thus, it is an Arithmetic sequence.
Since we have to find the sum of the sequence
Sum of sequence of a given Arithmetic sequence is given as :
.............(1)
But, first find the number of terms,
![a_n=a_0+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da_0%2B%28n-1%29d)
Put values, we get,
![\Rightarrow 1001=1+(n-1)2](https://tex.z-dn.net/?f=%5CRightarrow%201001%3D1%2B%28n-1%292)
![\Rightarrow 1001=1+2n-2](https://tex.z-dn.net/?f=%5CRightarrow%201001%3D1%2B2n-2)
![\Rightarrow 1001=2n-1](https://tex.z-dn.net/?f=%5CRightarrow%201001%3D2n-1)
![\Rightarrow 1001+1=2n](https://tex.z-dn.net/?f=%5CRightarrow%201001%2B1%3D2n)
![\Rightarrow 501=n](https://tex.z-dn.net/?f=%5CRightarrow%20501%3Dn)
Now put values,
,
and ![a_0=1](https://tex.z-dn.net/?f=a_0%3D1)
in (1), we get,
![S_n=(a_0+a_n)\times \frac{n}{2}](https://tex.z-dn.net/?f=S_n%3D%28a_0%2Ba_n%29%5Ctimes%20%5Cfrac%7Bn%7D%7B2%7D)
![\Rightarrow S_n=(1+1001)\times \frac{501}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20S_n%3D%281%2B1001%29%5Ctimes%20%5Cfrac%7B501%7D%7B2%7D)
![\Rightarrow S_n=(1002)\times \frac{501}{2}](https://tex.z-dn.net/?f=%5CRightarrow%20S_n%3D%281002%29%5Ctimes%20%5Cfrac%7B501%7D%7B2%7D)
![\Rightarrow S_n=251001](https://tex.z-dn.net/?f=%5CRightarrow%20S_n%3D251001)
Thus, the sum of the sequence 1+3+5+7+...1001 is 251001.
Answer:
the answer is c
Step-by-step explanation: